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Abstract

Limit theorems are established for some functionals of the distances between
two nodes in weighted random b-ary recursive trees. We consider the
depth of the nth node and of a random node, the distance between two
random nodes, the internal path length, and the Wiener index. As an
application, these limit results imply, by an imbedding argument, corresponding
limit theorems for further classes of random trees: plane-oriented recursive
trees and random linear recursive trees.